A Manager needs 4 different teams (named P, Q, R, S) for doing project

Question

GMATBusters’ Quant Quiz Question -1

For past quiz questions, click  here

A Manager needs 4 different teams (named P, Q, R, S) for doing projects A, B, C, D respectively. In how many different ways can a group of 8 people be divided into 4 teams of 2 people each for carrying out the Projects? 
A. 90 
B. 105 
c. 168 
D. 420 
E. 2520

GMATBusters · Answer

Official Solution:

The number of ways to divide m+n+p objects into three groups having m,n, and p objects, where each group has a specific name assigned to it, is (m+n+p)! x (number of arrangements possible for the names )!/(m! x n! x p!)

Here 8 persons to be divided into 4 groups of 2 people each.

So answer = 8!/(2!2!2!2!) = 2520 = Answer E

See this for the complete concept :  https://gmatclub.com/forum/dividing-objects-into-groups-combinations-266092.html

NikuHBS · Answer

8 people divided into 4 teams of 2 each can be done in
 \frac{8!}{2!*2!*2!*2!}  = 2520

Option E

urshi · Answer

Answer : Option E : 2520

ashwini2k6jha · Answer

ANSWER:B

GIVEN total number of people=8 and people are to be divided in 4 team (P,Q,R,S)of two people
total number of combination of selecting 2 people from 8 people in 4 team= 8C2X6C2X4C2X2C2
Now since in this combination numbers are repeated,so final answer is divided by 4!
Number of different ways a group of 8 people can be divided in 4 team of 2 people=8C2 X 6C2 X4C2 X2C2/4! =105

yashikaaggarwal · Answer

If we compute permutations of elements, the number would be: 8!

In this case, the permutation
A B C D E F G H 
would represent:
{A, B}, {C, D}, {E, F}, {G, H}

But that would be the same as:
{B, A}, {C, D}, {E, F}, {G, H}

That is, for any of the 4 groups, the order doesn’t matter… and you have 2 possible ways for every “pair”.
So, you have to divide by (2*2*2*2)

So, that would be:
8! / (2*2*2*2)

But that would be if the order of the 4 groups matters… if
{A, B}, {C, D}, {E, F}, {G, H}
is different from
{C, D}, {A, B}, {E, F}, {G, H}
Which is basically the same as the former but he {A, B} is in the “second group” instead of the “first group”.

If the order of the 4 groups doesn’t matter, then we have to divide by the number of ways you can order the 4 groups, that is, the permutations of 4 ‘elements’, which is: 4!

4*7*3*5*2*3 / 4! = 7*5*3 = 105

Answer is B

Posted from my mobile device

saurabh851 · Answer

ANS: B (105)

8C2 * 6C2 * 4C2 * 2C2/ 4!
= 105

Hope it is right....

KG04 · Answer

since 8 people are to be divided into 4 teams of 2 each 
8!/(2!)^4 = 2520

vtexcelgmat · Answer

ANSWER IS E

8C2 x 6C2 x 4C2

= 2520

MayankSingh · Answer

IMO E

Total No. of persons for selection = 8
Teams to be formed = 4
No. of people in each team = 2

Now, total ways of making team P = Select 2 out of 8 people = 8C2 = 28
Similarly. total ways of making team Q = Select 2 out of remaining 6 people = 6C2 = 15
For R = Select 2 out of remaining 4 people = 4C2 = 6
For S = Select 2 out of remaining 6 people = 2C2 = 1

Therefore, Total Possible ways to make the teams P,Q,R,S = 28x15x6x1= 2520

E. 2520

firas92 · Answer

Projects : --A--B--C--D--
Teams : --P--Q--R--S--

This is just the number of different arrangements in which we can make 4 teams of 2 people each from a group of 8 people

That is 8C2*6C2*4C2*2C2 = 28*15*6*1 = 2520

Answer is  (E)

Kinshook · Answer

Given: A Manager needs 4 different teams (named P, Q, R, S) for doing projects A, B, C, D respectively. 
Asked: In how many different ways can a group of 8 people be divided into 4 teams of 2 people each for carrying out the Projects? 
A. 90 
B. 105 
c. 168 
D. 420 
E. 2520

Let 8 persons be designated as:

P1 P2 Q1 Q2 R1 R2 S1 S2

Total number of different ways can a group of 8 people be divided into 4 teams of 2 people each for carrying out the Projects = 8!/2^4 = 2520

IMO E

Archit3110 · Answer

A Manager needs 4 different teams (named P, Q, R, S) for doing projects A, B, C, D respectively. In how many different ways can a group of 8 people be divided into 4 teams of 2 people each for carrying out the Projects?
A. 90
B. 105
c. 168
D. 420
E. 2520

total possible ways
8c2*6c2*4c2*2c2/ 4! ; 
solve we get 105
OPTION B

saumyagupta1602 · Answer

Out of 8 people select 2 people to form first team
then out of remaining (8-2=)6 people choose 2 people ..then 2 people from 4 and at last 2 from 2.
since there are 4 teams with identical team size=2 , we divide by 4!
{8C2 * 6C2 * 4C2 * 2C2 }/ 4!=105
P,Q,R and s=so multiply by 4!
=2520>> option E

Fightingspirit · Answer

Hello

E is the right answer

Totally 4 different teams have to be formed.So we cannot have any repetition.

1st : 8 C 2 *
2nd : 6 C 2 *
3rd : 4 C 2 *
4th : 2 C 2

Equals 2520.

Best

Posted from my mobile device

RiRa777 · Answer

We have 8 people to fit into 8 slots(4 groups * 2 members each) and, the number of ways that can happen is 8!. But, there are only 4 unique slots and rest is a replica of the first four. Something like this P, Q, R, S, P, Q, R, S. Now you can re-interpret what the question is asking, in how many ways can you arrange the letters of the word PPQQRRSS (remember MISSISSIPPI)? And the answer is, 8!/(2!2!2!2!)= 2520.

I figured out that there is another way to solve this with logic.

Step 1- Pick two members of group P from 8 people. Number of ways we can do that is 8C2= 28.
Step 2- Pick two members of the team Q from remaining 6 people. Number of ways we can do that is 6C2= 15.
Step 3- Pick members of team R from remaining 4 people. # Ways to do that is 4C2=6.
Step 4- Last two remaining form the group S.

Hence, the number of ways we can make 4 teams of 2 people each from 8 members = 28*15*6*1= 2520.

Hope it helps

fugaquasi · Answer

I was confused about this for a while but i figured it:

So we have to use the third type of question principle from here : https://gmatclub.com/forum/dividing-obj ... 66092.html

basically:

8 = 2+2+2+2
(how the groups are spread)

now the groups can be assigned to jobs in 4! ways since any group can do any job.

the number of ways will follow the formula : {(number of objects)! * (ways to distribute named groups)} / {(factorial of each group size) * (factorial of the number of repeated group sizes)}

this turns out to be: (8!*4!)/{(2!*2!*2!*2!)*4!}
=> 8!/2!*2!*2!*2! => 2520

In the terminology of the original explanation: m+n+p+q = 8, m=n=p=q=2,

{(4m)! x (number of arrangement possible for the names )!}/{(m! x n! x p! x q!) x (no. of groups having the same number of objects)!}

A Manager needs 4 different teams (named P, Q, R, S) for doing project

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

A Manager needs 4 different teams (named P, Q, R, S) for doing project

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards